Evaluate the two trigonometric functions using its period as an aid.
1. cos (9pi/2) = ?
Ans: 0
2. cos (-9pi/2) = ?
Ans: 0
I think they are both 0 because cos(t) = x.
Yes, they are both 0, but your reasoning baffles me
what is " cos(t) = x" supposed to mean ?
The hint was to use the period
9π/2
= 4π + 1/2 π
so we have 2 full rotations plus another half
cos(9π/2) = cos(π/2) = 0
cos(t) = x refers to the x-value found on the unit circle for the corresponding radian measure. So pi/2 has the x value of 0 on the unit circle.
To evaluate the two trigonometric functions using the period as an aid, we need to remember that the cosine function has a period of 2π.
1. For the first function, cos(9π/2), we can rewrite the angle as (4π + π/2). Since the cosine function has a period of 2π, adding any multiple of 2π to the angle does not change the cosine value. Therefore, cos(9π/2) is equal to cos(π/2).
The cosine value of π/2 is 0, so cos(9π/2) = 0.
2. For the second function, cos(-9π/2), we can rewrite the angle as (-4π - π/2). Again, adding or subtracting any multiple of 2π does not change the cosine value. So, cos(-9π/2) is equal to cos(-π/2).
The cosine value of -π/2 is also 0, so cos(-9π/2) = 0.
Therefore, both cos(9π/2) and cos(-9π/2) evaluate to 0.
To evaluate the given trigonometric functions, we can use the concept of the period of trigonometric functions. The period of a trigonometric function is the length of one complete cycle of the function. For the cosine function, its period is 2π.
1. For cos(9π/2), we can determine the equivalent angle within one period by dividing 9π/2 by 2π.
9π/2 ÷ 2π = 9/4 = 2 + 1/4
This means that 9π/2 is equivalent to 2 and 1/4 complete cycles of the cosine function. Since each complete cycle has a cosine value of 0 at some point, we can conclude that cos(9π/2) is also equal to 0.
2. For cos(-9π/2), we can determine the equivalent angle within one period by dividing -9π/2 by 2π.
-9π/2 ÷ 2π = -(9/4) = -2 - 1/4
This means that -9π/2 is equivalent to -2 and 1/4 complete cycles of the cosine function. Since each complete cycle has a cosine value of 0 at some point, we can conclude that cos(-9π/2) is also equal to 0.
Therefore, both cos(9π/2) and cos(-9π/2) have a value of 0.